Translations of tessellations

Rotations

Reflections

M.C. Escher

Reflection symmetry

Translation symmetry

Rotation symmetry

Glide reflection symmetry

NETS standards

Lesson plans

Evaluation

You will begin to notice many geometric shapes as you observe the world around you. Some of them are formed by nature, and others are made by man. They can all be very beautiful and interesting if you just take the time to look.

Tessellations

A tessellation is a tiled pattern formed by repeating figures to fill a plane without gaps or overlaps.

Tessellations are usually found on most tiled floors and ceilings, such as those found in kitchens and bathrooms. Most brick work used for building is made up of tessellations. Bees form tessellations when they make honeycombs.

There are also geometric properties involved in the formation of tessellations. Tessellations can be formed by translations, rotations, and reflections. M.C. Escher is known for his artwork based on tessellations. He was highly respected by mathematicians and scientists, but he did not consider himself a mathematician or an artist because he had no formal training in math or science.

Natural Geometric Figures

Many geometric shapes are formed by nature. As mentioned above, animals such as bees, can create these shapes. Think about the typical spider's web. Look at the patterns.

Tessellations are not the only figures formed naturally. It is also easy to identify types of symmetry seen around the world. Hold your hands up in front of you. Most people can see a mirror image, or what looks like a reflection of one hand. It is the same for your feet and most of the other body parts that we have two of.

Symmetry is the ability to move an object so that its image is an exact copy of the original object. There are four basic types of symmetry studied in geometry. These types of symmetries are reflection, translation, rotation, and glide reflection.

• The easiest type of symmetry to see is reflection symmetry. This type of symmetry is seen by viewing an object as if a mirror is placed on a line and the reflection from the mirror is the other side.

• Another type of symmetry seen is translational. Translational symmetry is the act of moving an object without turning or flipping it. When a car moves forward or backward, a change has taken place, but not on the car itself. It has been translated to a new location.

• Rotation means that an object is moving around a particular point. With rotational symmetry, an object moves around a point a certain number of degrees, without changing the original appearance of the object.

• The last type of symmetry discussed in this lesson is a glide reflection. A glide reflection is a combination of reflecting (flipping) and translating (sliding).

Tessellations and symmetry share many of the same properties.